Molecular Dynamics

概述

Molecular dynamics (MD) simulation computationally models the time evolution of molecular systems by integrating Newton's equations of motion. This skill covers two complementary tools:

• OpenMM (https://openmm.org/): High-performance MD simulation engine with GPU support, Python API, and flexible force field support
• MDAnalysis (https://mdanalysis.org/): Python library for reading, writing, and analyzing MD trajectories from all major simulation packages

Installation:

conda install -c conda-forge openmm mdanalysis nglview
# or
uv pip install openmm mdanalysis

使用時機

Use molecular dynamics when:

• Protein stability analysis: How does a mutation affect protein dynamics?
• Drug binding simulations: Characterize binding mode and residence time of a ligand
• Conformational sampling: Explore protein flexibility and conformational changes
• Protein-protein interaction: Model interface dynamics and binding energetics
• RMSD/RMSF analysis: Quantify structural fluctuations from a reference structure
• Free energy estimation: Compute binding free energy or conformational free energy
• Membrane simulations: Model proteins in lipid bilayers
• Intrinsically disordered proteins: Study IDR conformational ensembles

Core Workflow: OpenMM Simulation

Examples are illustrative and require system-specific preparation and validation. Synthetic checks cover the corrected timestep, thermostat, RMSF indexing, and periodic contact calculations; they do not establish protein/ligand equilibration.

1. System Preparation

from openmm.app import *
from openmm import *
from openmm.unit import *
import sys

def prepare_system_from_pdb(pdb_file, forcefield_name="amber14-all.xml",
                              water_model="amber14/tip3pfb.xml"):
    """
    Prepare an OpenMM system from a PDB file.

    Args:
        pdb_file: Path to cleaned PDB file (use PDBFixer for raw PDB files)
        forcefield_name: Force field XML file
        water_model: Water model XML file

    Returns:
        modeller, system
    """
    # Load PDB
    pdb = PDBFile(pdb_file)

    # Load force field
    forcefield = ForceField(forcefield_name, water_model)

    # Add hydrogens and solvate
    modeller = Modeller(pdb.topology, pdb.positions)
    modeller.addHydrogens(forcefield)

    # Add solvent box (10 Å padding, 150 mM NaCl)
    modeller.addSolvent(
        forcefield,
        model='tip3p',
        padding=10*angstroms,
        ionicStrength=0.15*molar
    )

    print(f"System: {modeller.topology.getNumAtoms()} atoms, "
          f"{modeller.topology.getNumResidues()} residues")

    # Create system
    system = forcefield.createSystem(
        modeller.topology,
        nonbondedMethod=PME,         # Particle Mesh Ewald for long-range electrostatics
        nonbondedCutoff=1.0*nanometer,
        constraints=HBonds,           # Constrain hydrogen bonds (allows 2 fs timestep)
        rigidWater=True,
        ewaldErrorTolerance=0.0005
    )

    return modeller, system

2. Energy Minimization

from openmm.app import *
from openmm import *
from openmm.unit import *

def minimize_energy(modeller, system, output_pdb="minimized.pdb",
                     max_iterations=1000, tolerance=10.0):
    """
    Energy minimize the system to remove steric clashes.

    Args:
        modeller: Modeller object with topology and positions
        system: OpenMM System
        output_pdb: Path to save minimized structure
        max_iterations: Maximum minimization steps
        tolerance: Convergence criterion in kJ/mol/nm

    Returns:
        simulation object with minimized positions
    """
    # Keep the integrator at 2 fs for the subsequent NVT/NPT examples.
    integrator = LangevinMiddleIntegrator(300*kelvin, 1/picosecond, 0.002*picoseconds)

    # Create simulation
    # Use GPU if available (CUDA or OpenCL), fall back to CPU
    try:
        platform = Platform.getPlatformByName('CUDA')
        properties = {'DeviceIndex': '0', 'Precision': 'mixed'}
    except Exception:
        try:
            platform = Platform.getPlatformByName('OpenCL')
            properties = {}
        except Exception:
            platform = Platform.getPlatformByName('CPU')
            properties = {}

    simulation = Simulation(
        modeller.topology, system, integrator,
        platform, properties
    )
    simulation.context.setPositions(modeller.positions)

    # Check initial energy
    state = simulation.context.getState(getEnergy=True)
    print(f"Initial energy: {state.getPotentialEnergy()}")

    # Minimize
    simulation.minimizeEnergy(
        tolerance=tolerance*kilojoules_per_mole/nanometer,
        maxIterations=max_iterations
    )

    state = simulation.context.getState(getEnergy=True, getPositions=True)
    print(f"Minimized energy: {state.getPotentialEnergy()}")

    # Save minimized structure
    with open(output_pdb, 'w') as f:
        PDBFile.writeFile(simulation.topology, state.getPositions(), f)

    return simulation

3. NVT Equilibration

from openmm.app import *
from openmm import *
from openmm.unit import *

def run_nvt_equilibration(simulation, n_steps=50000, temperature=300,
                            report_interval=1000, output_prefix="nvt"):
    """
    NVT equilibration: constant N, V, T.
    Equilibrate velocities to target temperature.

    Args:
        simulation: OpenMM Simulation (after minimization)
        n_steps: Number of MD steps (50000 × 2fs = 100 ps)
        temperature: Temperature in Kelvin
        report_interval: Steps between data reports
        output_prefix: File prefix for trajectory and log
    """
    # Add position restraints for backbone during NVT
    # (Optional: restraint heavy atoms)

    # Set both the thermostat target and initial velocities.
    simulation.integrator.setTemperature(temperature*kelvin)
    simulation.context.setVelocitiesToTemperature(temperature*kelvin)

    # Add reporters
    simulation.reporters = []

    # Log file
    simulation.reporters.append(
        StateDataReporter(
            f"{output_prefix}_log.txt",
            report_interval,
            step=True,
            potentialEnergy=True,
            kineticEnergy=True,
            temperature=True,
            volume=True,
            speed=True
        )
    )

    # DCD trajectory (compact binary format)
    simulation.reporters.append(
        DCDReporter(f"{output_prefix}_traj.dcd", report_interval)
    )

    print(f"Running NVT equilibration: {n_steps} steps ({n_steps*2/1000:.1f} ps)")
    simulation.step(n_steps)
    print("NVT equilibration complete")

    return simulation

4. NPT Equilibration and Production

def run_npt_production(simulation, n_steps=500000, temperature=300, pressure=1.0,
                        report_interval=5000, output_prefix="npt"):
    """
    NPT production run: constant N, P, T.

    Args:
        n_steps: Production steps (500000 × 2fs = 1 ns)
        temperature: Temperature in Kelvin
        pressure: Pressure in bar
        report_interval: Steps between reports
    """
    # Keep the Langevin thermostat and barostat at the same temperature.
    simulation.integrator.setTemperature(temperature*kelvin)
    # Add once to a simulation that does not already contain a barostat.
    system = simulation.context.getSystem()
    system.addForce(MonteCarloBarostat(pressure*bar, temperature*kelvin, 25))
    simulation.context.reinitialize(preserveState=True)

    # Update reporters
    simulation.reporters = []
    simulation.reporters.append(
        StateDataReporter(
            f"{output_prefix}_log.txt",
            report_interval,
            step=True,
            potentialEnergy=True,
            temperature=True,
            density=True,
            speed=True
        )
    )
    simulation.reporters.append(
        DCDReporter(f"{output_prefix}_traj.dcd", report_interval)
    )

    # Save checkpoints
    simulation.reporters.append(
        CheckpointReporter(f"{output_prefix}_checkpoint.chk", 50000)
    )

    print(f"Running NPT production: {n_steps} steps ({n_steps*2/1000000:.2f} ns)")
    simulation.step(n_steps)
    print("Production MD complete")
    return simulation

Trajectory Analysis with MDAnalysis

1. Load Trajectory

import MDAnalysis as mda
from MDAnalysis.analysis import rms, align, contacts
import numpy as np
import matplotlib.pyplot as plt

def load_trajectory(topology_file, trajectory_file):
    """
    Load an MD trajectory with MDAnalysis.

    Args:
        topology_file: PDB, PSF, or other topology file
        trajectory_file: DCD, XTC, TRR, or other trajectory
    """
    u = mda.Universe(topology_file, trajectory_file)
    print(f"Universe: {u.atoms.n_atoms} atoms, {u.trajectory.n_frames} frames")
    print(f"Time range: 0 to {u.trajectory.totaltime:.0f} ps")
    return u

2. RMSD Analysis

def compute_rmsd(u, selection="backbone", reference_frame=0):
    """
    Compute RMSD of selected atoms relative to reference frame.

    Args:
        u: MDAnalysis Universe
        selection: Atom selection string (MDAnalysis syntax)
        reference_frame: Frame index for reference structure

    Returns:
        numpy array of (time, rmsd) values
    """
    # Align trajectory to minimize RMSD
    aligner = align.AlignTraj(u, u, select=selection, in_memory=True)
    aligner.run()

    # Compute RMSD
    R = rms.RMSD(u, select=selection, ref_frame=reference_frame)
    R.run()

    rmsd_data = R.results.rmsd  # columns: frame, time, RMSD
    return rmsd_data

def plot_rmsd(rmsd_data, title="RMSD over time", output_file="rmsd.png"):
    """Plot RMSD over simulation time."""
    fig, ax = plt.subplots(figsize=(10, 4))
    ax.plot(rmsd_data[:, 1] / 1000, rmsd_data[:, 2], 'b-', linewidth=0.5)
    ax.set_xlabel("Time (ns)")
    ax.set_ylabel("RMSD (Å)")
    ax.set_title(title)
    ax.axhline(rmsd_data[:, 2].mean(), color='r', linestyle='--',
               label=f'Mean: {rmsd_data[:, 2].mean():.2f} Å')
    ax.legend()
    plt.tight_layout()
    plt.savefig(output_file, dpi=150)
    return fig

3. RMSF Analysis (Per-Residue Flexibility)

Make molecules whole across periodic boundaries and align the trajectory to the chosen reference before calling RMSF; RMSF does not perform alignment. Preserve segment/chain identity with residue IDs when reporting systems with repeated IDs.

def compute_rmsf(u, selection="backbone", start_frame=0):
    """
    Compute per-residue RMSF (flexibility).

    Returns:
        resids, rmsf_values arrays
    """
    # Select atoms
    atoms = u.select_atoms(selection)

    # Compute RMSF
    R = rms.RMSF(atoms)
    R.run(start=start_frame)

    # Average by residue
    resids = []
    rmsf_per_res = []
    for res in u.select_atoms(selection).residues:
        res_atoms = res.atoms.intersection(atoms)
        if len(res_atoms) > 0:
            resids.append(res.resid)
            # RMSF is indexed within the selected AtomGroup, not the Universe.
            rmsf_per_res.append(R.results.rmsf[atoms.resindices == res.ix].mean())

    return np.array(resids), np.array(rmsf_per_res)

4. Protein-Ligand Contacts

def analyze_contacts(u, protein_sel="protein", ligand_sel="resname LIG",
                      radius=4.5, start_frame=0):
    """
    Track protein-ligand contacts over trajectory.

    Args:
        radius: Contact distance cutoff in Angstroms
    """
    from MDAnalysis.lib.distances import distance_array

    protein = u.select_atoms(protein_sel)
    ligand = u.select_atoms(ligand_sel)

    contact_frames = []
    for ts in u.trajectory[start_frame:]:
        # Find protein atoms within radius of ligand
        distances = contacts.contact_matrix(
            distance_array(protein.positions, ligand.positions, box=ts.dimensions),
            radius,
        )
        contact_residues = set()
        for i in range(distances.shape[0]):
            if distances[i].any():
                contact_residues.add(protein.atoms[i].resid)
        contact_frames.append(contact_residues)

    return contact_frames

Force Field Selection Guide

System Preparation Tools

PDBFixer (for raw PDB files)

from pdbfixer import PDBFixer
from openmm.app import PDBFile

def fix_pdb(input_pdb, output_pdb, ph=7.0):
    """Fix common PDB issues: missing residues, atoms, add H, standardize."""
    fixer = PDBFixer(filename=input_pdb)
    fixer.findMissingResidues()
    fixer.findNonstandardResidues()
    fixer.replaceNonstandardResidues()
    fixer.removeHeterogens(True)    # Keep water; remove other heterogens (including ligands)
    fixer.findMissingAtoms()
    fixer.addMissingAtoms()
    fixer.addMissingHydrogens(ph)

    with open(output_pdb, 'w') as f:
        PDBFile.writeFile(fixer.topology, fixer.positions, f)

    return output_pdb

OpenFF Parameters for Small Molecules

# For ligand parameterization, use OpenFF toolkit or ACPYPE
# uv pip install openff-toolkit
from openff.toolkit import Molecule, ForceField as OFFForceField
from openff.interchange import Interchange

def parameterize_ligand(smiles, ff_name="openff-2.0.0.offxml"):
    """Generate OpenFF parameters (not GAFF2) for a small molecule."""
    mol = Molecule.from_smiles(smiles)
    mol.generate_conformers(n_conformers=1)

    off_ff = OFFForceField(ff_name)
    interchange = off_ff.create_interchange(mol.to_topology())
    return interchange

最佳實踐

• Always minimize before MD: Raw PDB structures have steric clashes
• Equilibrate before production: NVT (50–100 ps) → NPT (100–500 ps) → Production
• Use GPU: Simulations are 10–100× faster on GPU (CUDA/OpenCL)
• 2 fs timestep with HBonds constraints: Standard; use 4 fs with HMR (hydrogen mass repartitioning)
• Analyze only equilibrated trajectory: Choose burn-in from observables, stationarity, and replicate agreement; do not discard an arbitrary fixed percentage
• Save checkpoints: MD runs can fail; checkpoints allow restart
• Periodic boundary conditions: Required for solvated systems
• PME for electrostatics: More accurate than cutoff methods for charged systems

延伸資源

• OpenMM documentation: https://openmm.org/documentation.html
• MDAnalysis user guide: https://docs.mdanalysis.org/
• GROMACS (alternative MD engine): https://manual.gromacs.org/
• NAMD (alternative): https://www.ks.uiuc.edu/Research/namd/
• CHARMM-GUI (web-based system builder): https://charmm-gui.org/
• AmberTools (free Amber tools): https://ambermd.org/AmberTools.php
• OpenMM paper: Eastman P et al. (2017) PLOS Computational Biology. PMID: 28278240
• MDAnalysis paper: Michaud-Agrawal N et al. (2011) J Computational Chemistry. PMID: 21500218